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Texas Assessment of Math Knowledge and SkillsAnswer Key
Objective 6:
The student will demonstrate an understanding of
geometric relationships and
spatial reasoning.
G(b)(4) Geometric structure. The student uses a variety of
representations to describe geometric
relationships and solve problems .
(A) The student selects an appropriate representation ([concrete,] pictorial,
graphical, verbal, or
symbolic ) in order to solve problems.
G(c)(1)Geometric patterns. The student identifies,
analyzes, and describes patterns that emerge from
two and threedimensional geometric figures.
(A) The student uses numeric and geometric patterns to make generalizations
about geometric
properties, including properties of polygons , ratios in similar figures and
solids, and angle
relationships in polygons and circles.
(B) The student uses the properties of transformations and their compositions to
make
connections between mathematics and the real world in applications such as
tessellations
or fractals.
(C) The student identifies and applies patterns from right triangles to solve
problems, including
special right triangles (454590 and 306090) and triangles whose sides are
Pythagorean
triples.
G(e)(3) Congruence and the geometry of size. The student applies the
concept of congruence to
justify properties of figures and solve problems.
(A) The student uses congruence transformations to make conjectures and justify
properties of
geometric figures.
Objective 7:
The student will demonstrate an understanding of two 
and threedimensional
representations of geometric relationships and shapes.
G(d)(1) Dimensionality and the geometry of location. The student analyzes
the relationship between
threedimensional objects and related twodimensional representations and uses
these
representations to solve problems.
(B) The student uses nets to represent [and construct] threedimensional
objects.
(C) The student uses top, front, side, and corner views of threedimensional
objects to create
accurate and complete representations and solve problems.
G(d)(2) Dimensionality and the geometry of location. The student
understands that coordinate
systems provide convenient and efficient ways of representing geometric figures
and uses them
accordingly.
(A) The student uses one and twodimensional coordinate systems to represent
points, lines,
line segments , and figures.
(B) The student uses slopes and equations of lines to investigate geometric
relationships,
including parallel lines, perpendicular lines, and [special segments of]
triangles and other
polygons.
(C) The student [develops and] uses formulas including distance and midpoint.
G(e)(2) Congruence and the geometry of size. The student analyzes
properties and describes
relationships in geometric figures.
(D) The student analyzes the characteristics of threedimensional figures and
their component
parts.
Objective 8:
The student will demonstrate an understanding of the
concepts and uses of
measurement and similarity.
G(e)(1) Congruence and the geometry of size. The student extends
measurement concepts to find
area, perimeter, and volume in problem situations.
(A) The student finds area of polygons and composite figures.
(B) The student finds areas of sectors and arc lengths of circles using
proportional reasoning .
(C) The student [develops, extends and] uses the Pythagorean Theorem.
(D) The student finds surface area and volumes of prisms, pyramids, spheres,
cones, and
cylinders in problem situations.
G(f)(1) Similarity and the geometry of shape. The student applies the
concepts of similarity to justify
properties of figures and solve problems.
(A) The student uses similarity properties and transformations to [explore and]
justify conjectures
about geometric figures.
(B) The student uses ratios to solve problems involving similar figures.
(C) In a variety of ways, the student [develops,] applies, and justifies
triangle similarity
relationships, such as right triangle ratios, [ trigonometric ratios ,] and
Pythagorean triples.
(D) The student describes the effect on perimeter, area, and volume when length,
width, or
height of a threedimensional solid is changed and applies this idea in solving
problems.
Objective 9:
The student will demonstrate an understanding of
percents, proportional
relationships, probability, and statistics in application problems.
(8.3) Patterns, relationships, and algebraic thinking. The student
identifies proportional relationships
in problem situations and solves problems. The student is expected to
(B) estimate and find solutions to application problems involving percents and
proportional
relationships such as similarity and rates.
(8.11) Probability and statistics. The student applies the concepts of
theoretical and experimental
probability to make predictions. The student is expected to
(A) find the probabilities of compound events (dependent and independent); and
(B) use theoretical probabilities and experimental results to make predictions
and decisions .
(8.12) Probability and statistics. The student uses statistical
procedures to describe data. The
student is expected to
(A) select the appropriate measure of central tendency to describe a set of data
for a particular
purpose; and
(C) construct circle graphs, bar graphs, and histograms, with and without
technology.
(8.13) Probability and statistics. The student
evaluates predictions and conclusions based on
statistical data. The student is expected to
(B) recognize misuses of graphical or numerical information and evaluate
predictions and
conclusions based on data analysis.
Objective 10:
The student will demonstrate an understanding of the
mathematical processes
and tools used in problem solving.
(8.14) Underlying processes and mathematical tools. The student applies
Grade 8 mathematics to
solve problems connected to everyday experiences, investigations in other
disciplines, and activities
in and outside of school. The student is expected to
(A) identify and apply mathematics to everyday experiences, to activities in and
outside of school,
with other disciplines, and with other mathematical topics;
(B) use a problemsolving model that incorporates understanding the problem,
making a plan,
carrying out the plan, and evaluating the solution for reasonableness; and
(C) select or develop an appropriate problemsolving strategy from a variety of
different types ,
including drawing a picture , looking for a pattern, systematic guessing and
checking, acting
it out, making a table, working a simpler problem , or working backwards to solve
a problem.
(8.15) Underlying processes and mathematical tools. The student
communicates about Grade 8
mathematics through informal and mathematical language, representations, and
models. The
student is expected to
(A) communicate mathematical ideas using language, efficient tools, appropriate
units, and
graphical, numerical, physical, or algebraic mathematical models.
(8.16) Underlying processes and mathematical tools. The student uses
logical reasoning to make
conjectures and verify conclusions. The student is expected to
(A) make conjectures from patterns or sets of examples and nonexamples; and
(B) validate his/her conclusions using mathematical properties and
relationships.
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